Year: 2017
Type: preprint
Abstract: This paper introduces the notion of an excellent quotient, which is stronger than a universal geometric quotient. The main result is that for an action of a connected solvable group $G$ on an affine scheme Spec$(R)$ there exists a semi-invariant $f$ such that Spec$(R_f) \to$ Spec$((R_f)^G)$ is an excellent quotient. The paper contains an algorithm for computing $f$ and $(R_f)^G$. If $R$ is a polynomial ring over a field, the algorithm requires no Gröbner basis computations, and it also computes a presentation of $(R_f)^G$. In this case, $(R_f)^G$ is a complete intersection. The existence of an excellent quotient extends to actions on quasi-affine schemes.
Source: arXiv (Cornell University)
Author: Kemper, Gregor
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2774423623